Both Bank of Ireland and AIB have passed the stress tests carried out to establish how resilient they would be in difficult economic circumstances.
The test subjected the banks to a programme whereby the economy could deteriorate, and suffer further damage from problems with international sovereign loans.
Ninety-one banks across Europe were subjected to the test by the Committee of European Banking Supervisors. A total of seven failed.
In AIB's case, passing the test assumes that they would succeed in a €7.4bn plan to raise further capital by the end of the year.
If they fail to do so, the Government may have to step in to meet any shortfall in the capital requirements.
Bank of Ireland has already raised the capital required of it.
The banks had already passed more severe stress testing carried out by the Irish Financial Regulator in March.
The test was carried out under three scenarios: a benchmark scenario, an 'adverse' scenario and a worst-case scenario, which took into account the impact of potential losses on eurozone government bonds held by banks.
Bank of Ireland said that even in the third scenario, its Tier 1 capital ratio - a measure of banks' financial strength - would be 7.1%, well above the 6% needed to pass the test.
Analysts were watching to see how robust the latest European stress testing would be.
They feared that if too many banks got through, it would imply that the test would be meaningless.
Property lending specialist Hypo Real Estate was the only German bank to fail the stress tests. Five Spanish savings banks also failed to meet the criteria. A Greek bank state-controlled ATEbank
also failed the test.
France fared better, with all four of its major banks - BNP Paribas, Societe Generale, Credit Agricole and BPCE - passing with a clean bill of health.
Minister for Finance Brian Lenihan has welcomed the outcome of the tests for AIB and Bank of Ireland.
He said they vindicated the financial targets set for the banks by the Central Bank and Financial Regulator earlier this year.
Minister Lenihan said he welcomed the increased transparency that the EU-wide test had brought to the banking system.
The minister also said that the Financial Regulator was in close contact with the banks to assess the results of the test and their implications, and in particular any need for recapitalisation.
However, he said the results of the worst-case scenario in the tests should not be considered as representative of the current position, saying they were based on 'extreme assumptions rather than expected outcomes'.
Meanwhile, an analyst with BGC Partners Howard Wheeldon has said there has been some scepticism that the tests were not tough enough.